MAYBE proof of prog.inttrs # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IRSwT could not be shown: (0) IRSwT (1) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (2) IRSwT (3) IRSwTTerminationDigraphProof [EQUIVALENT, 2409 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 70 ms] (6) IRSwT (7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (8) IRSwT (9) TempFilterProof [SOUND, 109 ms] (10) IRSwT (11) IRSwTTerminationDigraphProof [EQUIVALENT, 0 ms] (12) AND (13) IRSwT (14) IntTRSCompressionProof [EQUIVALENT, 0 ms] (15) IRSwT (16) IRSwT (17) IntTRSCompressionProof [EQUIVALENT, 0 ms] (18) IRSwT ---------------------------------------- (0) Obligation: Rules: l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && -1 * x2 + x3 <= 0 && -1 * x2 + x3 <= 0 l3(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x10 <= x11 l3(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x19 <= x18 l4(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x28 = x28 l1(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x32 = x36 && 0 <= x37 && x37 <= 0 && x37 = x37 && x35 <= x34 && x34 <= x35 && -1 * x34 + x35 <= 0 && -1 * x34 + x35 <= 0 l5(x40, x41, x42, x43) -> l1(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 l1(x48, x49, x50, x51) -> l7(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x48 = x52 && x53 = x53 && x51 <= x50 && x50 <= x51 && -1 * x50 + x51 <= 0 && -1 * x50 + x51 <= 0 l7(x56, x57, x58, x59) -> l8(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && 1 + x57 <= 0 l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x65 l8(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x73 = x77 && x72 = x76 && x78 = 1 + x74 l6(x80, x81, x82, x83) -> l1(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 l1(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x88 = x92 && 0 <= x93 && x93 <= 0 && x93 = x93 && 0 <= -1 - x90 + x91 l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x99 = x103 && x98 = x102 && x97 = x101 && x96 = x100 l1(x104, x105, x106, x107) -> l11(x108, x109, x110, x111) :|: x107 = x111 && x106 = x110 && x104 = x108 && x109 = x109 && 0 <= -1 - x106 + x107 l11(x112, x113, x114, x115) -> l12(x116, x117, x118, x119) :|: x115 = x119 && x114 = x118 && x113 = x117 && x112 = x116 && 1 + x113 <= 0 l11(x120, x121, x122, x123) -> l12(x124, x125, x126, x127) :|: x123 = x127 && x122 = x126 && x121 = x125 && x120 = x124 && 1 <= x121 l12(x128, x129, x130, x131) -> l10(x132, x133, x134, x135) :|: x131 = x135 && x129 = x133 && x128 = x132 && x134 = 1 + x130 l10(x136, x137, x138, x139) -> l1(x140, x141, x142, x143) :|: x139 = x143 && x138 = x142 && x137 = x141 && x136 = x140 l13(x144, x145, x146, x147) -> l0(x148, x149, x150, x151) :|: x147 = x151 && x146 = x150 && x145 = x149 && x144 = x148 Start term: l13(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (1) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (2) Obligation: Rules: l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HAT0 = Result_4HATpost l1(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && -1 * x2 + x3 <= 0 && -1 * x2 + x3 <= 0 l3(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x10 <= x11 l3(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x19 <= x18 l4(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x28 = x28 l1(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x32 = x36 && 0 <= x37 && x37 <= 0 && x37 = x37 && x35 <= x34 && x34 <= x35 && -1 * x34 + x35 <= 0 && -1 * x34 + x35 <= 0 l5(x40, x41, x42, x43) -> l1(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 l1(x48, x49, x50, x51) -> l7(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x48 = x52 && x53 = x53 && x51 <= x50 && x50 <= x51 && -1 * x50 + x51 <= 0 && -1 * x50 + x51 <= 0 l7(x56, x57, x58, x59) -> l8(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && 1 + x57 <= 0 l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x65 l8(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x73 = x77 && x72 = x76 && x78 = 1 + x74 l6(x80, x81, x82, x83) -> l1(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 l1(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x88 = x92 && 0 <= x93 && x93 <= 0 && x93 = x93 && 0 <= -1 - x90 + x91 l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x99 = x103 && x98 = x102 && x97 = x101 && x96 = x100 l1(x104, x105, x106, x107) -> l11(x108, x109, x110, x111) :|: x107 = x111 && x106 = x110 && x104 = x108 && x109 = x109 && 0 <= -1 - x106 + x107 l11(x112, x113, x114, x115) -> l12(x116, x117, x118, x119) :|: x115 = x119 && x114 = x118 && x113 = x117 && x112 = x116 && 1 + x113 <= 0 l11(x120, x121, x122, x123) -> l12(x124, x125, x126, x127) :|: x123 = x127 && x122 = x126 && x121 = x125 && x120 = x124 && 1 <= x121 l12(x128, x129, x130, x131) -> l10(x132, x133, x134, x135) :|: x131 = x135 && x129 = x133 && x128 = x132 && x134 = 1 + x130 l10(x136, x137, x138, x139) -> l1(x140, x141, x142, x143) :|: x139 = x143 && x138 = x142 && x137 = x141 && x136 = x140 l13(x144, x145, x146, x147) -> l0(x148, x149, x150, x151) :|: x147 = x151 && x146 = x150 && x145 = x149 && x144 = x148 Start term: l13(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) ---------------------------------------- (3) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l0(Result_4HAT0, tmp_7HAT0, x_5HAT0, y_6HAT0) -> l1(Result_4HATpost, tmp_7HATpost, x_5HATpost, y_6HATpost) :|: y_6HAT0 = y_6HATpost && x_5HAT0 = x_5HATpost && tmp_7HAT0 = tmp_7HATpost && Result_4HAT0 = Result_4HATpost (2) l1(x, x1, x2, x3) -> l3(x4, x5, x6, x7) :|: x3 = x7 && x2 = x6 && x1 = x5 && x = x4 && -1 * x2 + x3 <= 0 && -1 * x2 + x3 <= 0 (3) l3(x8, x9, x10, x11) -> l4(x12, x13, x14, x15) :|: x11 = x15 && x10 = x14 && x9 = x13 && x8 = x12 && 1 + x10 <= x11 (4) l3(x16, x17, x18, x19) -> l4(x20, x21, x22, x23) :|: x19 = x23 && x18 = x22 && x17 = x21 && x16 = x20 && 1 + x19 <= x18 (5) l4(x24, x25, x26, x27) -> l2(x28, x29, x30, x31) :|: x27 = x31 && x26 = x30 && x25 = x29 && x28 = x28 (6) l1(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x32 = x36 && 0 <= x37 && x37 <= 0 && x37 = x37 && x35 <= x34 && x34 <= x35 && -1 * x34 + x35 <= 0 && -1 * x34 + x35 <= 0 (7) l5(x40, x41, x42, x43) -> l1(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 (8) l1(x48, x49, x50, x51) -> l7(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x48 = x52 && x53 = x53 && x51 <= x50 && x50 <= x51 && -1 * x50 + x51 <= 0 && -1 * x50 + x51 <= 0 (9) l7(x56, x57, x58, x59) -> l8(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && 1 + x57 <= 0 (10) l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x65 (11) l8(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x73 = x77 && x72 = x76 && x78 = 1 + x74 (12) l6(x80, x81, x82, x83) -> l1(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 (13) l1(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x88 = x92 && 0 <= x93 && x93 <= 0 && x93 = x93 && 0 <= -1 - x90 + x91 (14) l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x99 = x103 && x98 = x102 && x97 = x101 && x96 = x100 (15) l1(x104, x105, x106, x107) -> l11(x108, x109, x110, x111) :|: x107 = x111 && x106 = x110 && x104 = x108 && x109 = x109 && 0 <= -1 - x106 + x107 (16) l11(x112, x113, x114, x115) -> l12(x116, x117, x118, x119) :|: x115 = x119 && x114 = x118 && x113 = x117 && x112 = x116 && 1 + x113 <= 0 (17) l11(x120, x121, x122, x123) -> l12(x124, x125, x126, x127) :|: x123 = x127 && x122 = x126 && x121 = x125 && x120 = x124 && 1 <= x121 (18) l12(x128, x129, x130, x131) -> l10(x132, x133, x134, x135) :|: x131 = x135 && x129 = x133 && x128 = x132 && x134 = 1 + x130 (19) l10(x136, x137, x138, x139) -> l1(x140, x141, x142, x143) :|: x139 = x143 && x138 = x142 && x137 = x141 && x136 = x140 (20) l13(x144, x145, x146, x147) -> l0(x148, x149, x150, x151) :|: x147 = x151 && x146 = x150 && x145 = x149 && x144 = x148 Arcs: (1) -> (2), (6), (8), (13), (15) (2) -> (4) (3) -> (5) (4) -> (5) (6) -> (7) (7) -> (2), (6), (8), (13), (15) (8) -> (9), (10) (9) -> (11) (10) -> (11) (11) -> (12) (12) -> (2), (6), (8), (13), (15) (13) -> (14) (14) -> (2), (6), (8), (13), (15) (15) -> (16), (17) (16) -> (18) (17) -> (18) (18) -> (19) (19) -> (2), (6), (8), (13), (15) (20) -> (1) This digraph is fully evaluated! ---------------------------------------- (4) Obligation: Termination digraph: Nodes: (1) l1(x32, x33, x34, x35) -> l5(x36, x37, x38, x39) :|: x35 = x39 && x34 = x38 && x32 = x36 && 0 <= x37 && x37 <= 0 && x37 = x37 && x35 <= x34 && x34 <= x35 && -1 * x34 + x35 <= 0 && -1 * x34 + x35 <= 0 (2) l6(x80, x81, x82, x83) -> l1(x84, x85, x86, x87) :|: x83 = x87 && x82 = x86 && x81 = x85 && x80 = x84 (3) l8(x72, x73, x74, x75) -> l6(x76, x77, x78, x79) :|: x75 = x79 && x73 = x77 && x72 = x76 && x78 = 1 + x74 (4) l7(x64, x65, x66, x67) -> l8(x68, x69, x70, x71) :|: x67 = x71 && x66 = x70 && x65 = x69 && x64 = x68 && 1 <= x65 (5) l7(x56, x57, x58, x59) -> l8(x60, x61, x62, x63) :|: x59 = x63 && x58 = x62 && x57 = x61 && x56 = x60 && 1 + x57 <= 0 (6) l1(x48, x49, x50, x51) -> l7(x52, x53, x54, x55) :|: x51 = x55 && x50 = x54 && x48 = x52 && x53 = x53 && x51 <= x50 && x50 <= x51 && -1 * x50 + x51 <= 0 && -1 * x50 + x51 <= 0 (7) l9(x96, x97, x98, x99) -> l1(x100, x101, x102, x103) :|: x99 = x103 && x98 = x102 && x97 = x101 && x96 = x100 (8) l1(x88, x89, x90, x91) -> l9(x92, x93, x94, x95) :|: x91 = x95 && x90 = x94 && x88 = x92 && 0 <= x93 && x93 <= 0 && x93 = x93 && 0 <= -1 - x90 + x91 (9) l10(x136, x137, x138, x139) -> l1(x140, x141, x142, x143) :|: x139 = x143 && x138 = x142 && x137 = x141 && x136 = x140 (10) l12(x128, x129, x130, x131) -> l10(x132, x133, x134, x135) :|: x131 = x135 && x129 = x133 && x128 = x132 && x134 = 1 + x130 (11) l11(x120, x121, x122, x123) -> l12(x124, x125, x126, x127) :|: x123 = x127 && x122 = x126 && x121 = x125 && x120 = x124 && 1 <= x121 (12) l11(x112, x113, x114, x115) -> l12(x116, x117, x118, x119) :|: x115 = x119 && x114 = x118 && x113 = x117 && x112 = x116 && 1 + x113 <= 0 (13) l1(x104, x105, x106, x107) -> l11(x108, x109, x110, x111) :|: x107 = x111 && x106 = x110 && x104 = x108 && x109 = x109 && 0 <= -1 - x106 + x107 (14) l5(x40, x41, x42, x43) -> l1(x44, x45, x46, x47) :|: x43 = x47 && x42 = x46 && x41 = x45 && x40 = x44 Arcs: (1) -> (14) (2) -> (1), (6), (8), (13) (3) -> (2) (4) -> (3) (5) -> (3) (6) -> (4), (5) (7) -> (1), (6), (8), (13) (8) -> (7) (9) -> (1), (6), (8), (13) (10) -> (9) (11) -> (10) (12) -> (10) (13) -> (11), (12) (14) -> (1), (6), (8), (13) This digraph is fully evaluated! ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: l1(x104:0, x105:0, x106:0, x107:0) -> l1(x104:0, x109:0, 1 + x106:0, x107:0) :|: 0 <= -1 - x106:0 + x107:0 && x109:0 > 0 l1(x48:0, x49:0, x50:0, x50:0) -> l1(x48:0, x53:0, 1 + x50:0, x50:0) :|: x53:0 < 0 && 0 >= -1 * x50:0 + x50:0 l1(x100:0, x89:0, x102:0, x103:0) -> l1(x100:0, x101:0, x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x, x1, x2, x3) -> l1(x, x4, 1 + x2, x3) :|: 0 <= -1 - x2 + x3 && x4 < 0 l1(x32:0, x33:0, x34:0, x34:0) -> l1(x32:0, x37:0, x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 l1(x5, x6, x7, x7) -> l1(x5, x8, 1 + x7, x7) :|: x8 > 0 && 0 >= -1 * x7 + x7 ---------------------------------------- (7) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: l1(x1, x2, x3, x4) -> l1(x3, x4) ---------------------------------------- (8) Obligation: Rules: l1(x106:0, x107:0) -> l1(1 + x106:0, x107:0) :|: 0 <= -1 - x106:0 + x107:0 && x109:0 > 0 l1(x50:0, x50:0) -> l1(1 + x50:0, x50:0) :|: x53:0 < 0 && 0 >= -1 * x50:0 + x50:0 l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x2, x3) -> l1(1 + x2, x3) :|: 0 <= -1 - x2 + x3 && x4 < 0 l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 l1(x7, x7) -> l1(1 + x7, x7) :|: x8 > 0 && 0 >= -1 * x7 + x7 ---------------------------------------- (9) TempFilterProof (SOUND) Used the following sort dictionary for filtering: l1(INTEGER, INTEGER) Replaced non-predefined constructor symbols by 0.The following proof was generated: # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given IntTRS could not be shown: - IntTRS - PolynomialOrderProcessor Rules: l1(x106:0, x107:0) -> l1(c, x107:0) :|: c = 1 + x106:0 && (0 <= -1 - x106:0 + x107:0 && x109:0 > 0) l1(x50:0, x50:0) -> l1(c1, x50:0) :|: c1 = 1 + x50:0 && (x53:0 < 0 && 0 >= -1 * x50:0 + x50:0) l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x2, x3) -> l1(c2, x3) :|: c2 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 < 0) l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 l1(x7, x7) -> l1(c3, x7) :|: c3 = 1 + x7 && (x8 > 0 && 0 >= -1 * x7 + x7) Found the following polynomial interpretation: [l1(x, x1)] = -x + x1 The following rules are decreasing: l1(x106:0, x107:0) -> l1(c, x107:0) :|: c = 1 + x106:0 && (0 <= -1 - x106:0 + x107:0 && x109:0 > 0) l1(x50:0, x50:0) -> l1(c1, x50:0) :|: c1 = 1 + x50:0 && (x53:0 < 0 && 0 >= -1 * x50:0 + x50:0) l1(x2, x3) -> l1(c2, x3) :|: c2 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 < 0) l1(x7, x7) -> l1(c3, x7) :|: c3 = 1 + x7 && (x8 > 0 && 0 >= -1 * x7 + x7) The following rules are bounded: l1(x106:0, x107:0) -> l1(c, x107:0) :|: c = 1 + x106:0 && (0 <= -1 - x106:0 + x107:0 && x109:0 > 0) l1(x50:0, x50:0) -> l1(c1, x50:0) :|: c1 = 1 + x50:0 && (x53:0 < 0 && 0 >= -1 * x50:0 + x50:0) l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x2, x3) -> l1(c2, x3) :|: c2 = 1 + x2 && (0 <= -1 - x2 + x3 && x4 < 0) l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 l1(x7, x7) -> l1(c3, x7) :|: c3 = 1 + x7 && (x8 > 0 && 0 >= -1 * x7 + x7) - IntTRS - PolynomialOrderProcessor - IntTRS Rules: l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 ---------------------------------------- (10) Obligation: Rules: l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 ---------------------------------------- (11) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 (2) l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 Arcs: (1) -> (1) (2) -> (2) This digraph is fully evaluated! ---------------------------------------- (12) Complex Obligation (AND) ---------------------------------------- (13) Obligation: Termination digraph: Nodes: (1) l1(x34:0, x34:0) -> l1(x34:0, x34:0) :|: 0 >= -1 * x34:0 + x34:0 && x37:0 > -1 && x37:0 < 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (14) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (15) Obligation: Rules: l1(x34:0:0, x34:0:0) -> l1(x34:0:0, x34:0:0) :|: 0 >= -1 * x34:0:0 + x34:0:0 && x37:0:0 > -1 && x37:0:0 < 1 ---------------------------------------- (16) Obligation: Termination digraph: Nodes: (1) l1(x102:0, x103:0) -> l1(x102:0, x103:0) :|: x101:0 < 1 && x101:0 > -1 && 0 <= -1 - x102:0 + x103:0 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (17) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (18) Obligation: Rules: l1(x102:0:0, x103:0:0) -> l1(x102:0:0, x103:0:0) :|: x101:0:0 < 1 && x101:0:0 > -1 && 0 <= -1 - x102:0:0 + x103:0:0